We define a new invariant for shift equivalence of sofic shifts. This invariant, that we call the syntactic graph of a sofic shift, is the directed acyclic graph of characteristic groups of the non null regular D-classes of the syntactic semigroup of the shift.

We present a decomposition formula for the weighted zeta function of an irregular covering of a graph by its weighted L-functions. Moreover, we give a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph. As an application, we discuss the structure of balanced coverings of signed graphs.

Equivalence relations on the edge set of a graph G that satisfy restrictive conditions on chordless squares play a crucial role in the theory of Cartesian graph products and graph bundles. We show here that such relations in a natural way induce equitable partitions on the vertex set of G, which in turn give rise to quotient graphs that can have a rich product structure even if G itself is prime.

We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph which is reducible by some finite sequence of these moves, to a graph with no edges is called a knot graph. We show that the class of knot graphs strictly contains the set of delta-wye graphs. We prove that the dimension of the intersection of the cycle and cocycl...

This paper derived single-valued neutrosophic graphs from single-valued neutrosophic hypergraphs via strong equivalence relation. We show that any weak single-valued neutrosophic graph is a derived single-valued neutrosophic graph and any linear weak single-valued neutrosophic tree is an extendable linear single-valued neutrosophic tree.

Combinatorial auctions (CAs) are an important mechanism for allocating multiple goods while allowing self-interested agents to specify preferences over bundles of items. Winner determination for a CA is known to be NP-complete. However, restricting the problem can allow us to solve winner determination in polynomial time. These restrictions sometimes apply to the CA’s representation. There are ...

We introduce and study the problem MUTUAL PLANAR DUALITY, which asks for two planar graphs G1 and G2 whether G1 can be embedded such that its dual is isomorphic to G2. Our algorithmic main result is an NP-completeness proof for the general case and a linear-time algorithm for biconnected graphs. To shed light onto the combinatorial structure of the duals of a planar graph, we consider the commo...

The problem of eecient characterization of inclusion neighbourhood is crucial for some methods of learning (equivalence classes of) Bayesian networks. In this paper, neighbouring equivalence classes of a given equivalence class of Bayesian networks are characterized eeciently by means of the respective essential graph. The characterization reveals hidded internal structure of the inclusion neig...

We introduce two new techniques to the analysis on fractals. One is based on the presentation of the fractal as the boundary of a countable Gromov hyperbolic graph, whereas the other one consists in taking all possible “backward” extensions of the above hyperbolic graph and considering them as the classes of a discrete equivalence relation on an appropriate compact space. Illustrating these tec...

Equivalence Classes of Circuit Mutants for Experimental Design Debabrata Ghosh Franc Brglez CBL (Collaborative Benchmarking Lab), Dept. of Computer Science, Box 7550 NC State University, Raleigh, NC 27695, USA http://www.cbl.ncsu.edu/ Abstract { Experimental Design, as de ned in science and manufacturing, relies on data sets that belong to well-de ned equivalence classes. This paper introduces ...